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How fast are we actually going?

  1. Mar 20, 2012 #1
    OK, I am brave enough to risk sounding like some kid who doesn't get secondary physics, let alone tertiary physics, with this question, but please bare with me.

    Given galaxies at the edge of the horizon of our universe appear to be accelerating away from us at greater velocities, surely we know that it is at least possible that it is us who is accelerating away from them at increasing velocities (yes, I know there is no pure observer since Einstein).

    Since a body at 12 billion light years from earth is speeding away so quickly, surely, with the rate of expansion of the universe increasing, our galaxy must be travelling at this rate from these distant galaxies at an exponential rate right now, given we have been part of this increasing acceleration for the past 12 billion years.

    The inflationary period is a very short time period, so we can't be looking back into it.

    So would it not be correct to look at a distant source like UDFy-38135539 and assume that we are now accelerating away from it at an exponential speed way higher than the red shift was measuring 12 billion years ago?

    Please forgive what might seem like an childish mistake.
  2. jcsd
  3. Mar 20, 2012 #2
    We are not accelerating within our own reference frame. We are at rest with regards to the CMB, which any other observer will observe from their FoR (Every galaxy is the center of its own OU with expansion moving outwards.)

    Distant galaxies can be receeding from us >c. As to them we would also appear to be moving >c. There are no prerferential reference frames though - so while we can observe expansion >c this is not "acceleration" through space so GR still holds up.

    Hopefully we will get some knowledgeable posters here as this is something I would like to explore a little bit further.
  4. Mar 20, 2012 #3


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    Well that's not true. There is most certainly a CMB dipole anisotropy.

    You appear to have read Einstein, but not fully grasped Einstein. We here, sitting on the Earth, observe some distant galaxy to be speeding away from us. But we can turn the situation around and imagine if we were in the shoes of that distant galaxy. As you suggest, they would see US speeding away from them! Actually, this is not Einstein at all, but rather simple Galilean relativity. The point is that the state of motion is relative to the observer. To ask how fast we are 'actually' moving presupposes the existence of a fixed reference frame against which we can measure our velocity -- Enter Einstein saying such a thing is not possible. We can say, as Cosmo Novice suggests, that we have a velocity with respect to the Cosmic Microwave Background radiation, but this is about as close as you can get.

    Another topic I think you are touching on is that the light we receive from a distant galaxy was emitted many billions of years in the past, and in that time the physical galaxy has surely continued on with the expansion of the universe, and is now much further away. This is absolutely true! The galaxy as we see it is as it was (to take your number) 12 billion years ago, not today. We cannot know what it is like 'today', as the photons need to take AT LEAST 12 billion years to reach us!
  5. Mar 21, 2012 #4
    I did not caveat my earlier point and mention this is caused by Earths actual kinemtaic movement through space, rather than a result of expansion. I should have made that more clear and you are correct in pointing it out as an important distinction.
  6. Mar 21, 2012 #5


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    Given that we are at the temporal edge of the universe [the most ancient point in the observable universe], your deduction is logical [albeit irrelevant].
  7. Mar 22, 2012 #6
    "We cannot know what it is like 'today', as the photons need to take AT LEAST 12 billion years to reach us!"

    Well, yes, I imagine there is a lot we don't know about what the last 12 billion years has done to that galaxy, but we do know, at the very least, that the velocity between us and the galaxy has increased hugely, since we know that the rate of the universe's expansion is increasing.

    Which means it would be possible, assuming the galaxy still exists, to calculate what the current the velocity would be, even if that galaxy would have passed beyond the observable horizon many billions of years ago.

    I guess I am just curious as to whether anyone has done such a theoretical calculation.

    The article below suggests that galaxies one day will appear to exceed c receding away from us.

    Does that mean that some of the galaxies we have observed would be already doing this now, theoretically?

  8. Mar 22, 2012 #7
    You can use this link for calculating recession speeds based on redgarbages. As you can see there are galaxies which we can currently observe but are now receeding >c.

  9. Mar 22, 2012 #8


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    Cosmo Novice suggestion is good, Daniel. Learn to use those online cosmos calculators. they are surprisingly easy. The one Novice suggests requires you to put in two numbers to start with (matter density .27 and lambda .73 or so) then put in a redshift.

    Those are just standard parameters of the model that cosmologists use. Anything like that (say .25 and .75) will work OK and give about the same answers.

    You can skip that priming step if you go to Jorry's version of the calculator (he's a PF regular).
    He puts the default values of the two parameters in for you, to save trouble.
    So then you just put in a redshift. He already has the redshift of the CMB in the box. You change that to whatever you want, and press calculate.

    My best advice would be to train yourself to think in terms of the "CMB rest" reference frame---according to which none of the galaxies are moving very much, they only have comparatively small random individual motions. This is the most widely used perspective or frame of reference in cosmology. Most everything is defined from the standpoint of CMB rest.

    Observers at CMB rest all over the universe can synchronize their clocks to standard universe time (the time that cosmologists normally use for modeling the cosmos) and so they have an idea of synchonicity and can talk about the distance between two things *at a particular moment of time*. (Socalled "proper distance".) Hubble law about recession rates is defined using proper distance. Recession rates are what you are working to understand right now, so you better learn about the basic underlying ideas of CMB rest and proper distance.

    This does not sound reality-based, it sounds more like imagination taking off from the VERBAL descriptions that popularizers dish out to the public. Let's use Jorry's calculator to find out what the real situation would be for a galaxy whose light has taken 12 billion years to reach us.

    Try different redshifts in the calculator until you find one that gives a light travel time of 12 billion years. Then see what the recession rate was at the moment the light was emitted and started on its way to us. And it will also tell you the recession rate today, as we receive the light.

    ON ITS OWN the light would have traveled 12 billion lightyears (in a nonexpanding U) but the expansion will have added to that. I think the calculator is clear enough but if something isn't clear please tell us!

    Jorry's calculator is in my signature where it says "cosmocalc"
    Last edited: Mar 22, 2012
  10. Mar 22, 2012 #9


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    Daniel, just to work out your example, using Jorry's calculator (the "cosmocalc" link in my signature at the end of the post) I get that the galaxy of your example must have a redshift of 3.7.

    Because that gives that the light "on its own" went 12 billion LY. The travel time was 12 billion years. Jorry really should label that box "travel time" and make the units years instead of lightyears, but nobody is perfect :biggrin:

    I'll see if that agrees with what the calculator Novice suggested gives. Good idea to check for agreement. We'd be in a fix if the online cosmology calculators gave different answers!

    Incidentally it says 1.92 and 1.67 for the recession rates of the galaxy then, and now. So the recession rate has DECLINED.

    The verbal stimulus that popularizers give to the public imagination can be misleading. It is not real information. Based on words read, Daniel gathered that the recession rate would now be "increased hugely" from what it was back then. But it is less, and both rates are quite modest, only between one and two times the speed of light.

    RECESSION RATES ARE NOT "SPEEDS" OF MOTION THRU THE SPACE DEFINED BY CMB REST they are just rates of proper distances increase that occur naturally in the dynamic geometry of general rel. It is quite usual for such rates of distance growth to be some multiple of c. Like the 1.67 c in Daniel's example. And the growth of distances hasn't been accelerating during the entire history of the U. That's another misconception the verbal popularizations promote.

    I checked the other calculator and after you put in the standard numbers .27 and .73 it gives essentially the same answer for redshift 3.7, namely recession rate 1.91c back then (light emitted) and 1.67c now (light received).

    Don't go anywhere without a cosmo redshift calculator. :biggrin:
    Last edited: Mar 22, 2012
  11. Mar 22, 2012 #10


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    Daniel, you asked How fast are we actually going?

    The question makes sense in the CMB rest frame that cosmologists use, and it is a good one.

    The answer is that the solar system is going 370 kilometers per second in the direction marked by the stars of the constellation Leo.

    That is a little more than one thousandth of the speed of light. It's no big deal. Most of the individual random motions of galaxies are roughly that size, a few hundred km/s.

    One thousandth is a tenth of a percent. We know the solar system is going in that direction at around a tenth of a percent of the speed of light because the CMB is a tenth of a percent warmer in that direction.

    Our antenna horns can measure the cosmic background temperature very precisely and it is remarkably uniform---except for this Doppler hotspot ahead (and the corresponding Doppler coldspot astern of us). We are approaching the ancient light that is coming towards us from the Leo direction. We go to meet the ancient light, so it is warmer.

    I'd say this is about the simplest and most beautiful fact in the whole science of cosmology.
    I hope you like it too. This hotspot/coldspot in the sky is called the "CMB dipole" and some earlier posters in your thread mentioned it, using its technical name.
    Last edited: Mar 22, 2012
  12. Mar 22, 2012 #11


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    I wake to sleep, and take my waking slow
    I feel my fate in what I cannot fear.
    I learn by going where I have to go.

    We think by feeling, what is there to know?
    I hear my being dance from ear to ear:
    I wake to sleep, and take my waking slow.

    Of those so close beside me, which are you?
    God bless the ground! I shall walk softly there,
    and learn by going where I have to go.

    [that's all I know of it by heart, it's a little bit of a poem in a Medieval rhyme-form by a Michigan man named Ted Roethke and it describes his coming to understand himself other people and life in a way that cosmology reminds me of. Cosmology is the human species on this planet gradually instinctively groping to understand its self and place in what surrounds us...we feel the slight warmth in Leo of the ancient light...and gradually come to comprehend the rest frame established by the ancient cloud of gas whose glow it was...]

    Full Roethke waking poem
    a friend's favorite YouTube
    Last edited: Mar 22, 2012
  13. Mar 23, 2012 #12
    OK, thanks, everyone for your combined learning and wisdom. I didn't think to look for an online red shift calculator.

    And, yes, I obviously am a victim of taking popularisers too literally (or misunderstanding them).

    Wonderful links. Thanks again!
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